Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAdaptive Robust Large Volatility Matrix Estimation Based on High-Frequency Financial Data
162
0
0.0
(
0
)
Added by
Minseok Shin
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order moment assumption for observed log-returns, which cannot account for the heavy tail phenomenon of stock returns. Recently, a robust estimator was developed to handle heavy-tailed distributions with some bounded fourth-moment assumption. However, we often observe that log-returns have heavier tail distribution than the finite fourth-moment and that the degrees of heaviness of tails are heterogeneous over the asset and time period. In this paper, to deal with the heterogeneous heavy-tailed distributions, we develop an adaptive robust integrated volatility estimator that employs pre-averaging and truncation schemes based on jump-diffusion processes. We call this an adaptive robust pre-averaging realized volatility (ARP) estimator. We show that the ARP estimator has a sub-Weibull tail concentration with only finite 2$alpha$-th moments for any $alpha>1$. In addition, we establish matching upper and lower bounds to show that the ARP estimation procedure is optimal. To estimate large integrated volatility matrices using the approximate factor model, the ARP estimator is further regularized using the principal orthogonal complement thresholding (POET) method. The numerical study is conducted to check the finite sample performance of the ARP estimator.
rate research
Read More
We consider high-dimensional measurement errors with high-frequency data. Our focus is on recovering the covariance matrix of the random errors with optimality. In this problem, not all components of the random vector are observed at the same time and the measurement errors are latent variables, leading to major challenges besides high data dimensionality. We propose a new covariance matrix estimator in this context with appropriate localization and thresholding. By developing a new technical device integrating the high-frequency data feature with the conventional notion of $alpha$-mixing, our analysis successfully accommodates the challenging serial dependence in the measurement errors. Our theoretical analysis establishes the minimax optimal convergence rates associated with two commonly used loss functions. We then establish cases when the proposed localized estimator with thresholding achieves the minimax optimal convergence rates. Considering that the variances and covariances can be small in reality, we conduct a second-order theoretical analysis that further disentangles the dominating bias in the estimator. A bias-corrected estimator is then proposed to ensure its practical finite sample performance. We illustrate the promising empirical performance of the proposed estimator with extensive simulation studies and a real data analysis.
In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We study a Lasso-type method for high dimensional precision matrix estimation and derive general error bounds under the weak sparsity condition. The common irrepresentable condition is relaxed and the results are applicable to the weak sparse matrix. As applications, we study the precision matrix estimation for the heavy-tailed data, the non-paranormal data, and the matrix data with the Lasso-type method.
We consider nonparametric inference of finite dimensional, potentially non-pathwise differentiable target parameters. In a nonparametric model, some examples of such parameters that are always non pathwise differentiable target parameters include probability density functions at a point, or regression functions at a point. In causal inference, under appropriate causal assumptions, mean counterfactual outcomes can be pathwise differentiable or not, depending on the degree at which the positivity assumption holds. In this paper, given a potentially non-pathwise differentiable target parameter, we introduce a family of approximating parameters, that are pathwise differentiable. This family is indexed by a scalar. In kernel regression or density estimation for instance, a natural choice for such a family is obtained by kernel smoothing and is indexed by the smoothing level. For the counterfactual mean outcome, a possible approximating family is obtained through truncation of the propensity score, and the truncation level then plays the role of the index. We propose a method to data-adaptively select the index in the family, so as to optimize mean squared error. We prove an asymptotic normality result, which allows us to derive confidence intervals. Under some conditions, our estimator achieves an optimal mean squared error convergence rate. Confidence intervals are data-adaptive and have almost optimal width. A simulation study demonstrates the practical performance of our estimators for the inference of a causal dose-response curve at a given treatment dose.
We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma prior on its values. This leads to a straightforward procedure for posterior inference via an MCMC procedure. We give theoretical performance guarantees (contraction rates for the posterior) for the Bayesian estimate in terms of the regularity of the unknown volatility function. We illustrate the method on synthetic and real data examples.
High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real high-dimensional time-series data. Recently [Sun, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed errors. They discover that the robustification parameter of the Huber loss should adapt to the sample size, the dimensionality, and the moments of the heavy-tailed errors. We progress in a vertical direction and justify AHR on dependent observations. Specifically, we consider an important dependence structure -- Markov dependence. Our results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
